Some of this is getting too complicated.

In ground effect the wing's collecting air (incompresible as noted) between it and the ground. We all know that this is going to result in added lift as the air tries to escape, but the wing keeps collecting new air between it and the ground.

If you're finding that you need formulas or exotic theory to figure out ground effect, get a paper bag, fill it with air, tie off the open end, then sit on it.

If ground affect had some other magic to it, then near the ground the wing could be flown at negative AOA and there'd still be lift. But there isn't. AOA is needed to trap air between the wing and the ground.